1. Notes: 13-2 Repetitions and Circular Permutations
How many different arrangements can you make using the letters WOW?
three??
OWW
WOW
WWO
This is correct!!

2. linear arrangement with repetitions:
The number of permutations of n objects of which p are alike and q are alike: _n!_ p!q!
Example#1: Waikiki has _7! arrangements,
2!3!
which is a total of 420 different permutations.
divide by
the repetitions)

3. From yesterday: linear arrangement = n! (permutation)
Now consider a circular permutation:
If n objects are arranged in a circle without a reference point, then there are (n-1)! permutations.

4. Example#2: If 4 people sit at a square table, how many arrangements are there?
(4-1)! 3! = 6 1 2 3 4
 These are all considered the same arrangement, just rotated differently.

5. Example#3: If 4 people sit at a square table, how many arrangements are there if someone wants to sit next to the window?
(4)! = 24 1 2 3 4
W i n d o w
These are now different arrangements because the window is a reference point and it creates a linear permutation.